ExtremaPC_Hyperbola Class Reference

Point-Hyperbola extrema computation. More...

#include <ExtremaPC_Hyperbola.hxx>

Public Member Functions
	ExtremaPC_Hyperbola (const gp_Hypr &theHyperbola)
	Constructor with hyperbola geometry (infinite).
	ExtremaPC_Hyperbola (const gp_Hypr &theHyperbola, const ExtremaPC::Domain1D &theDomain)
	Constructor with hyperbola geometry and parameter domain.
	ExtremaPC_Hyperbola (const ExtremaPC_Hyperbola &)=delete
	Copy constructor is deleted.
ExtremaPC_Hyperbola &	operator= (const ExtremaPC_Hyperbola &)=delete
	Copy assignment operator is deleted.
	ExtremaPC_Hyperbola (ExtremaPC_Hyperbola &&)=default
	Move constructor.
ExtremaPC_Hyperbola &	operator= (ExtremaPC_Hyperbola &&)=default
	Move assignment operator.
gp_Pnt	Value (double theU) const
	Evaluates point on hyperbola at parameter using cached geometry.
bool	IsBounded () const
	Returns true if domain is bounded.
const ExtremaPC::Domain1D &	Domain () const
	Returns the domain (only valid if IsBounded() is true).
const ExtremaPC::Result &	Perform (const gp_Pnt &theP, double theTol, ExtremaPC::SearchMode theMode=ExtremaPC::SearchMode::MinMax) const
	Compute extrema between point P and the hyperbola. Uses domain specified at construction time.
const ExtremaPC::Result &	PerformWithEndpoints (const gp_Pnt &theP, double theTol, ExtremaPC::SearchMode theMode=ExtremaPC::SearchMode::MinMax) const
	Compute extrema between point P and the hyperbola arc including endpoints. Uses domain specified at construction time.
const gp_Hypr &	Hyperbola () const
	Returns the hyperbola geometry.

Detailed Description

Point-Hyperbola extrema computation.

Computes the extrema between a 3D point and a hyperbola. Uses quartic polynomial solving via MathPoly::Quartic with substitution.

The algorithm:

1. Projects point P onto the hyperbola plane -> Pp
2. For hyperbola C(u) = (R*cosh(u), r*sinh(u)) with major radius R and minor radius r, substitutes v = e^u to convert the transcendental equation to a polynomial: ((R^2 + r^2)/4) * v^4 - ((X*R + Y*r)/2) * v^3 + ((X*R - Y*r)/2) * v - ((R^2 + r^2)/4) = 0
3. Filters positive roots (v > 0) and converts back via u = ln(v)

Note

A hyperbola can have up to 4 extrema.

The domain is fixed at construction time for optimal performance. For infinite hyperbola, construct without domain or with nullopt.

Constructor & Destructor Documentation

ExtremaPC_Hyperbola() [1/4]

ExtremaPC_Hyperbola::ExtremaPC_Hyperbola ( const gp_Hypr & theHyperbola )

inlineexplicit

Constructor with hyperbola geometry (infinite).

Parameters

[in]

theHyperbola

the hyperbola to compute extrema for

ExtremaPC_Hyperbola() [2/4]

ExtremaPC_Hyperbola::ExtremaPC_Hyperbola ( const gp_Hypr & theHyperbola, const ExtremaPC::Domain1D & theDomain )

inline

Constructor with hyperbola geometry and parameter domain.

Parameters

[in]	theHyperbola	the hyperbola to compute extrema for
[in]	theDomain	parameter domain (fixed for all queries)

ExtremaPC_Hyperbola() [3/4]

ExtremaPC_Hyperbola::ExtremaPC_Hyperbola ( const ExtremaPC_Hyperbola & )

delete

Copy constructor is deleted.

ExtremaPC_Hyperbola() [4/4]

ExtremaPC_Hyperbola::ExtremaPC_Hyperbola ( ExtremaPC_Hyperbola && )

default

Move constructor.

Member Function Documentation

Domain()

const ExtremaPC::Domain1D & ExtremaPC_Hyperbola::Domain ( ) const

inline

Returns the domain (only valid if IsBounded() is true).

Hyperbola()

const gp_Hypr & ExtremaPC_Hyperbola::Hyperbola ( ) const

inline

Returns the hyperbola geometry.

IsBounded()

bool ExtremaPC_Hyperbola::IsBounded ( ) const

inline

Returns true if domain is bounded.

operator=() [1/2]

ExtremaPC_Hyperbola & ExtremaPC_Hyperbola::operator= ( const ExtremaPC_Hyperbola & )

delete

Copy assignment operator is deleted.

operator=() [2/2]

ExtremaPC_Hyperbola & ExtremaPC_Hyperbola::operator= ( ExtremaPC_Hyperbola && )

default

Move assignment operator.

Perform()

const ExtremaPC::Result & ExtremaPC_Hyperbola::Perform ( const gp_Pnt & theP, double theTol, ExtremaPC::SearchMode theMode = ExtremaPC::SearchMode::MinMax ) const

inline

Compute extrema between point P and the hyperbola. Uses domain specified at construction time.

Parameters

theP	query point
theTol	tolerance for duplicate detection
theMode	search mode (MinMax, Min, or Max)

Returns

const reference to result containing extrema

PerformWithEndpoints()

const ExtremaPC::Result & ExtremaPC_Hyperbola::PerformWithEndpoints ( const gp_Pnt & theP, double theTol, ExtremaPC::SearchMode theMode = ExtremaPC::SearchMode::MinMax ) const

inline

Compute extrema between point P and the hyperbola arc including endpoints. Uses domain specified at construction time.

Parameters

theP	query point
theTol	tolerance for duplicate detection
theMode	search mode (MinMax, Min, or Max)

Returns

const reference to result containing interior + endpoint extrema

Value()

gp_Pnt ExtremaPC_Hyperbola::Value ( double theU ) const

inline

Evaluates point on hyperbola at parameter using cached geometry.

Parameters

theU

parameter

Returns

point on hyperbola

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The documentation for this class was generated from the following file:

• ExtremaPC_Hyperbola.hxx